Measurement of the top-quark mass in the all-hadronic
channel using the full CDF data set
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Citation
Aaltonen, T. et al. “Measurement of the Top-Quark Mass in the
All-Hadronic Channel Using the Full CDF Data Set.” Physical
Review D 90.9 (2014): n. pag. © 2014 American Physical Society
As Published
http://dx.doi.org/10.1103/PhysRevD.90.091101
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American Physical Society
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Final published version
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Wed May 25 15:50:33 EDT 2016
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http://hdl.handle.net/1721.1/92278
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RAPID COMMUNICATIONS
PHYSICAL REVIEW D 90, 091101(R) (2014)
Measurement of the top-quark mass in the all-hadronic channel
using the full CDF data set
T. Aaltonen,21 S. Amerio,39b,39a D. Amidei,31 A. Anastassov,15,v A. Annovi,17 J. Antos,12 G. Apollinari,15 J. A. Appel,15
T. Arisawa,52 A. Artikov,13 J. Asaadi,47 W. Ashmanskas,15 B. Auerbach,2 A. Aurisano,47 F. Azfar,38 W. Badgett,15
T. Bae,25 A. Barbaro-Galtieri,26 V. E. Barnes,43 B. A. Barnett,23 P. Barria,41c,41a P. Bartos,12 M. Bauce,39b,39a F. Bedeschi,41a
S. Behari,15 G. Bellettini,41b,41a J. Bellinger,54 D. Benjamin,14 A. Beretvas,15 A. Bhatti,45 K. R. Bland,5 B. Blumenfeld,23
A. Bocci,14 A. Bodek,44 D. Bortoletto,43 J. Boudreau,42 A. Boveia,11 L. Brigliadori,6b,6a C. Bromberg,32 E. Brucken,21
J. Budagov,13 H. S. Budd,44 K. Burkett,15 G. Busetto,39b,39a P. Bussey,19 P. Butti,41b,41a A. Buzatu,19 A. Calamba,10
S. Camarda,4 M. Campanelli,28 F. Canelli,11,cc B. Carls,22 D. Carlsmith,54 R. Carosi,41a S. Carrillo,16,l B. Casal,9,j
M. Casarsa,48a A. Castro,6b,6a P. Catastini,20 D. Cauz,48b,48c,48a V. Cavaliere,22 A. Cerri,26,e L. Cerrito,28,q Y. C. Chen,1
M. Chertok,7 G. Chiarelli,41a G. Chlachidze,15 K. Cho,25 D. Chokheli,13 A. Clark,18 C. Clarke,53 M. E. Convery,15
J. Conway,7 M. Corbo,15,y M. Cordelli,17 C. A. Cox,7 D. J. Cox,7 M. Cremonesi,41a D. Cruz,47 J. Cuevas,9,x R. Culbertson,15
N. d’Ascenzo,15,u M. Datta,15,ff P. de Barbaro,44 L. Demortier,45 M. Deninno,6a M. D’Errico,39b,39a F. Devoto,21
A. Di Canto,41b,41a B. Di Ruzza,15,p J. R. Dittmann,5 S. Donati,41b,41a M. D’Onofrio,27 M. Dorigo,48d,48a A. Driutti,48b,48c,48a
K. Ebina,52 R. Edgar,31 A. Elagin,47 R. Erbacher,7 S. Errede,22 B. Esham,22 S. Farrington,38 J. P. Fernández Ramos,29
R. Field,16 G. Flanagan,15,s R. Forrest,7 M. Franklin,20 J. C. Freeman,15 H. Frisch,11 Y. Funakoshi,52 C. Galloni,41b,41a
A. F. Garfinkel,43 P. Garosi,41c,41a H. Gerberich,22 E. Gerchtein,15 S. Giagu,46a V. Giakoumopoulou,3 K. Gibson,42
C. M. Ginsburg,15 N. Giokaris,3 P. Giromini,17 V. Glagolev,13 D. Glenzinski,15 M. Gold,34 D. Goldin,47 A. Golossanov,15
G. Gomez,9 G. Gomez-Ceballos,30 M. Goncharov,30 O. González López,29 I. Gorelov,34 A. T. Goshaw,14 K. Goulianos,45
E. Gramellini,6a C. Grosso-Pilcher,11 R. C. Group,51,15 J. Guimaraes da Costa,20 S. R. Hahn,15 J. Y. Han,44 F. Happacher,17
K. Hara,49 M. Hare,50 R. F. Harr,53 T. Harrington-Taber,15,m K. Hatakeyama,5 C. Hays,38 J. Heinrich,40 M. Herndon,54
A. Hocker,15 Z. Hong,47 W. Hopkins,15,f S. Hou,1 R. E. Hughes,35 U. Husemann,55 M. Hussein,32,aa J. Huston,32
G. Introzzi,41d,41e,41a M. Iori,46b,46a A. Ivanov,7,o E. James,15 D. Jang,10 B. Jayatilaka,15 E. J. Jeon,25 S. Jindariani,15
M. Jones,43 K. K. Joo,25 S. Y. Jun,10 T. R. Junk,15 M. Kambeitz,24 T. Kamon,25,47 P. E. Karchin,53 A. Kasmi,5 Y. Kato,37,n
W. Ketchum,11,gg J. Keung,40 B. Kilminster,15,cc D. H. Kim,25 H. S. Kim,25 J. E. Kim,25 M. J. Kim,17 S. H. Kim,49
S. B. Kim,25 Y. J. Kim,25 Y. K. Kim,11 N. Kimura,52 M. Kirby,15 K. Knoepfel,15 K. Kondo,52,* D. J. Kong,25
J. Konigsberg,16 A. V. Kotwal,14 M. Kreps,24 J. Kroll,40 M. Kruse,14 T. Kuhr,24 M. Kurata,49 A. T. Laasanen,43
S. Lammel,15 M. Lancaster,28 K. Lannon,35,w G. Latino,41c,41a H. S. Lee,25 J. S. Lee,25 S. Leo,41a S. Leone,41a
J. D. Lewis,15 A. Limosani,14,r E. Lipeles,40 A. Lister,18,a H. Liu,51 Q. Liu,43 T. Liu,15 S. Lockwitz,55 A. Loginov,55
D. Lucchesi,39b,39a A. Lucà,17 J. Lueck,24 P. Lujan,26 P. Lukens,15 G. Lungu,45 J. Lys,26 R. Lysak,12,d R. Madrak,15
P. Maestro,41c,41a S. Malik,45 G. Manca,27,b A. Manousakis-Katsikakis,3 L. Marchese,6a,ii F. Margaroli,46a P. Marino,41d,41e
K. Matera,22 M. E. Mattson,53 A. Mazzacane,15 P. Mazzanti,6a R. McNulty,27,i A. Mehta,27 P. Mehtala,21 C. Mesropian,45
T. Miao,15 D. Mietlicki,31 A. Mitra,1 H. Miyake,49 S. Moed,15 N. Moggi,6a C. S. Moon,15,y R. Moore,15,dd,ee
M. J. Morello,41d,41a A. Mukherjee,15 Th. Muller,24 P. Murat,15 M. Mussini,6b,6a J. Nachtman,15,m Y. Nagai,49 J. Naganoma,52
I. Nakano,36 A. Napier,50 J. Nett,47 C. Neu,51 T. Nigmanov,42 L. Nodulman,2 S. Y. Noh,25 O. Norniella,22 L. Oakes,38
S. H. Oh,14 Y. D. Oh,25 I. Oksuzian,51 T. Okusawa,37 R. Orava,21 L. Ortolan,4 C. Pagliarone,48a E. Palencia,9,e P. Palni,34
V. Papadimitriou,15 W. Parker,54 G. Pauletta,48b,48c,48a M. Paulini,10 C. Paus,30 T. J. Phillips,14 E. Pianori,40 J. Pilot,7
K. Pitts,22 C. Plager,8 L. Pondrom,54 S. Poprocki,15,f K. Potamianos,26 A. Pranko,26 F. Prokoshin,13,z F. Ptohos,17,g
G. Punzi,41b,41a I. Redondo Fernández,29 P. Renton,38 M. Rescigno,46a F. Rimondi,6a,* L. Ristori,41a,15 A. Robson,19
T. Rodriguez,40 S. Rolli,50,h M. Ronzani,41b,41a R. Roser,15 J. L. Rosner,11 F. Ruffini,41c,41a A. Ruiz,9 J. Russ,10 V. Rusu,15
W. K. Sakumoto,44 Y. Sakurai,52 L. Santi,48b,48c,48a K. Sato,49 V. Saveliev,15,u A. Savoy-Navarro,15,y P. Schlabach,15
E. E. Schmidt,15 T. Schwarz,31 L. Scodellaro,9 F. Scuri,41a S. Seidel,34 Y. Seiya,37 A. Semenov,13 F. Sforza,48b,48a
S. Z. Shalhout,7 T. Shears,27 P. F. Shepard,42 M. Shimojima,49,t M. Shochet,11 I. Shreyber-Tecker,33 A. Simonenko,13
K. Sliwa,50 J. R. Smith,7 F. D. Snider,15 H. Song,42 V. Sorin,4 R. St. Denis,19,* M. Stancari,15 D. Stentz,15,v J. Strologas,34
Y. Sudo,49 A. Sukhanov,15 I. Suslov,13 K. Takemasa,49 Y. Takeuchi,49 J. Tang,11 M. Tecchio,31 P. K. Teng,1 J. Thom,15,f
E. Thomson,40 V. Thukral,47 D. Toback,47 S. Tokar,12 K. Tollefson,32 T. Tomura,49 D. Tonelli,15,e S. Torre,17 D. Torretta,15
P. Totaro,39a M. Trovato,41d,41a F. Ukegawa,49 S. Uozumi,25 F. Vázquez,16,l G. Velev,15 C. Vellidis,15 C. Vernieri,41d,41a
M. Vidal,43 R. Vilar,9 J. Vizán,9,bb M. Vogel,34 G. Volpi,17 P. Wagner,40 R. Wallny,15,j S. M. Wang,1 D. Waters,28
W. C. Wester III,15 D. Whiteson,40,c A. B. Wicklund,2 S. Wilbur,7 H. H. Williams,40 J. S. Wilson,31 P. Wilson,15
B. L. Winer,35 P. Wittich,15,f S. Wolbers,15 H. Wolfe,35 T. Wright,31 X. Wu,18 Z. Wu,5 K. Yamamoto,37 D. Yamato,37
T. Yang,15 U. K. Yang,25 Y. C. Yang,25 W.-M. Yao,26 G. P. Yeh,15 K. Yi,15,m J. Yoh,15 K. Yorita,52 T. Yoshida,37,k G. B. Yu,14
I. Yu,25 A. M. Zanetti,48a Y. Zeng,14 C. Zhou,14 and S. Zucchelli6b,6a
(CDF Collaboration)
1550-7998=2014=90(9)=091101(8)
091101-1
© 2014 American Physical Society
RAPID COMMUNICATIONS
T. AALTONEN et al.
PHYSICAL REVIEW D 90, 091101(R) (2014)
1
Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2
Argonne National Laboratory, Argonne, Illinois 60439, USA
3
University of Athens, 157 71 Athens, Greece
4
Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona,
E-08193 Bellaterra (Barcelona), Spain
5
Baylor University, Waco, Texas 76798, USA
6a
Istituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy
6b
University of Bologna, I-40127 Bologna, Italy
7
University of California, Davis, Davis, California 95616, USA
8
University of California, Los Angeles, Los Angeles, California 90024, USA
9
Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
10
Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
11
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
12
Comenius University, 842 48 Bratislava, Slovakia and Slovakia
and Institute of Experimental Physics, 040 01 Kosice, Slovakia
13
Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
14
Duke University, Durham, North Carolina 27708, USA
15
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
16
University of Florida, Gainesville, Florida 32611, USA
17
Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
18
University of Geneva, CH-1211 Geneva 4, Switzerland
19
Glasgow University, Glasgow G12 8QQ, United Kingdom
20
Harvard University, Cambridge, Massachusetts 02138, USA
21
Division of High Energy Physics, Department of Physics, University of Helsinki, FIN-00014 Helsinki,
Finland and Helsinki Institute of Physics, FIN-00014 Helsinki, Finland
22
University of Illinois, Urbana, Illinois 61801, USA
23
The Johns Hopkins University, Baltimore, Maryland 21218, USA
24
Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany
25
Center for High Energy Physics, Kyungpook National University, Daegu 702-701, Korea; Seoul
National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea; Korea
Institute of Science and Technology Information, Daejeon 305-806, Korea; Chonnam National University,
Gwangju 500-757, Korea; Chonbuk National University,
Jeonju 561-756, Korea; and Ewha Womans University, Seoul 120-750, Korea
26
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
27
University of Liverpool, Liverpool L69 7ZE, United Kingdom
28
University College London, London WC1E 6BT, United Kingdom
29
Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
30
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
31
University of Michigan, Ann Arbor, Michigan 48109, USA
32
Michigan State University, East Lansing, Michigan 48824, USA
33
Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
34
University of New Mexico, Albuquerque, New Mexico 87131, USA
35
The Ohio State University, Columbus, Ohio 43210, USA
36
Okayama University, Okayama 700-8530, Japan
37
Osaka City University, Osaka 558-8585, Japan
38
University of Oxford, Oxford OX1 3RH, United Kingdom
39a
Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
39b
University of Padova, I-35131 Padova, Italy
40
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
41a
Istituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy
41b
University of Pisa, I-56127 Pisa, Italy
41c
University of Siena, I-56127 Pisa, Italy
41d
Scuola Normale Superiore, I-56127 Pisa, Italy
41e
INFN Pavia, I-27100 Pavia, Italy
41f
University of Pavia, I-27100 Pavia, Italy
42
University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
43
Purdue University, West Lafayette, Indiana 47907, USA
44
University of Rochester, Rochester, New York 14627, USA
45
The Rockefeller University, New York, New York 10065, USA
46a
Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy
091101-2
RAPID COMMUNICATIONS
MEASUREMENT OF THE TOP-QUARK MASS IN THE ALL- …
PHYSICAL REVIEW D 90, 091101(R) (2014)
46b
Sapienza Università di Roma, I-00185 Roma, Italy
Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University,
College Station, Texas 77843, USA
48a
Istituto Nazionale di Fisica Nucleare Trieste, I-33100 Udine, Italy
48b
Gruppo Collegato di Udine, I-33100 Udine, Italy
48c
University of Udine, I-33100 Udine, Italy
48d
University of Trieste, I-34127 Trieste, Italy
49
University of Tsukuba, Tsukuba, Ibaraki 305, Japan
50
Tufts University, Medford, Massachusetts 02155, USA
51
University of Virginia, Charlottesville, Virginia 22906, USA
52
Waseda University, Tokyo 169, Japan
53
Wayne State University, Detroit, Michigan 48201, USA
54
University of Wisconsin, Madison, Wisconsin 53706, USA
55
Yale University, New Haven, Connecticut 06520, USA
(Received 18 September 2014; published 18 November 2014)
47
The top-quark mass M top is measured using top quark-antiquark pairs produced in proton-antiproton
collisions at a center-of-mass energy of 1.96 TeV and that decay into a fully hadronic final state. The full
data set collected with the CDF II detector at the Fermilab Tevatron Collider, corresponding to an integrated
luminosity of 9.3 fb−1 , is used. Events are selected that have six to eight jets, at least one of which is
identified as having originated from a b quark. In addition, a multivariate algorithm, containing multiple
kinematic variables as inputs, is used to discriminate signal events from background events due to QCD
multijet production. Templates for the reconstructed top-quark mass are combined in a likelihood fit to
measure M top with a simultaneous calibration of the jet energy scale. A value of M top ¼ 175.07 þ1.55
1.19ðstatÞ −1.58
ðsystÞ GeV=c2 is obtained for the top-quark mass.
DOI: 10.1103/PhysRevD.90.091101
PACS numbers: 14.65.Ha, 13.85.Ni, 13.85.Qk
*
Deceased.
Visitor from University of British Columbia, Vancouver, BC V6T 1Z1, Canada.
Visitor from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy.
c
Visitor from University of California Irvine, Irvine, California 92697, USA.
d
Visitor from Institute of Physics, Academy of Sciences of the Czech Republic, 182 21, Czech Republic.
e
Visitor from CERN, CH-1211 Geneva, Switzerland.
f
Visitor from Cornell University, Ithaca, New York 14853, USA.
g
Visitor from University of Cyprus, Nicosia CY-1678, Cyprus.
h
Visitor from Office of Science, U.S. Department of Energy, Washington, DC 20585, USA.
i
Visitor from University College Dublin, Dublin 4, Ireland.
j
Visitor from ETH, 8092 Zürich, Switzerland.
k
Visitor from University of Fukui, Fukui City, Fukui Prefecture 910-0017, Japan.
l
Visitor from Universidad Iberoamericana, Lomas de Santa Fe, C.P. 01219, Distrito Federal, México.
m
Visitor from University of Iowa, Iowa City, Iowa 52242, USA.
n
Visitor from Kinki University, Higashi-Osaka City 577-8502, Japan.
o
Visitor from Kansas State University, Manhattan, Kansas 66506, USA.
p
Visitor from Brookhaven National Laboratory, Upton, New York 11973, USA.
q
Visitor from Queen Mary, University of London, London E1 4NS, United Kingdom.
r
Visitor from University of Melbourne, Victoria 3010, Australia.
s
Visitor from Muons, Inc., Batavia, Illinois 60510, USA.
t
Visitor from Nagasaki Institute of Applied Science, Nagasaki 851-0193, Japan.
u
Visitor from National Research Nuclear University, Moscow 115409, Russia.
v
Visitor from Northwestern University, Evanston, Illinois 60208, USA.
w
Visitor from University of Notre Dame, Notre Dame, Indiana 46556, USA.
x
Visitor from Universidad de Oviedo, E-33007 Oviedo, Spain.
y
Visitor from CNRS-IN2P3, Paris F-75205, France.
z
Visitor from Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile.
aa
Visitor from The University of Jordan, Amman 11942, Jordan.
bb
Visitor from Universite Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium.
cc
Visitor from University of Zürich, 8006 Zürich, Switzerland.
dd
Visitor from Massachusetts General Hospital, Boston, Massachusetts 02114, USA.
ee
Visitor from Harvard Medical School, Boston, Massachusetts 02114, USA.
ff
Visitor from Hampton University, Hampton, Virginia 23668, USA.
gg
Visitor from Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA.
hh
Visitor from Università degli Studi di Napoli Federico I, I-80138 Napoli, Italy.
a
b
091101-3
RAPID COMMUNICATIONS
T. AALTONEN et al.
PHYSICAL REVIEW D 90, 091101(R) (2014)
The mass of the top quark, M top , is a fundamental
parameter of the standard model (SM). Furthermore, the
measured value of M top is comparable to the mass scale of
electroweak-symmetry breaking, suggesting that the top
quark may play a special role in this phenomenon, either in
the SM or in new physics processes beyond the SM [1,2].
After the Higgs-boson discovery by the ATLAS and CMS
experiments [3,4], precise measurements of Mtop are
critical inputs to global electroweak fits that assess the
self-consistency of the SM [5], and are crucial for determining the stability of the vacuum [6].
In pp̄ collisions at 1.96 TeV center-of-mass energy, top
quarks are produced predominantly in pairs (tt̄), with each
top quark decaying into a W boson and a bottom quark with
a probability of nearly 100% [7]. For this analysis candidate
events are selected in which both W bosons decay to a
quark-antiquark pair (tt̄ → W þ bW − b̄ → q1 q̄2 bq3 q̄4 b̄).
This final state, the all-hadronic channel, comprises 46%
of all tt̄ final states, which is larger than the probabilities of
all other individual tt̄ decay channels. However, it suffers
from large multijet background due to quantum chromodynamics (QCD) production, which exceeds tt̄ production
by 3 orders of magnitude. The principal advantage of
this analysis channel, though, is that a full kinematic
reconstruction of the tt̄ state is possible, as there are no
undetected particles. In this paper, we present a measurement of the top-quark mass using the full data set collected
by the CDF experiment in 2002–2011, with the same event
selection as in Ref. [8]. Apart from the nearly twofold
increase in integrated luminosity, additional improvements
come from the use of a new Monte Carlo generator. The
simulated samples used for the tt̄ signal are now produced
by POWHEG [9], a next-to-leading-order generator in the
strong-interaction coupling interfaced with PYTHIA [10] for
parton shower evolution and hadronization.
The CDF II detector consists of high-precision
tracking systems for vertex and charged-particle track
reconstruction, surrounded by electromagnetic and hadronic calorimeters for energy measurement. Muon subsystems are located outside the calorimeter for muon
detection. A detailed description can be found in
Ref. [11]. The data correspond to the full integrated
luminosity of 9.3 fb−1 . Events are selected with a multijet
trigger [12], and retained only if they have no wellidentified energetic electron or muon. A jet is identified
as a cluster of calorimeter
energies fficontained within a cone
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
of radius ΔR ≡ ðΔηÞ2 þ ðΔϕÞ2 ¼ 0.4, where Δη and
Δϕ are the distances in pseudorapidity [13] and azimuthal
angle between a tower center and the cluster axis. Jet
energies are corrected for a number of effects that bias their
measurement [14].
A total of about 11.4 × 106 events are selected in data
having six to eight jets, each with a transverse energy of at
least 15 GeV and satisfying a pseudorapidity requirement
of jηj ≤ 2.0. Events with neutrinos in the final state are
suppressed by the requirement that the missing transverse
energy ET [13]
is small
to its resolution, and
ffiffiffiffiffiffiffiffiffiffiffi
ffi with respect
pP
P
1
satisfies ET =
ET < 3 GeV2 , where ET is the sum of
the transverse energy of all jets. Of these events, less than
16 000 are expected to originate from tt̄ signal. The signal
purity is improved through an artificial neural network,
which takes as input a set of kinematic and jet-shape
variables [12]. The neural network is trained using simulated tt̄ events for the signal and the selected candidate
events for the multijet background, since the fraction of tt̄
events in the candidate sample is still negligible (on the
order of 1=700). The value of the output node N out is used
as a discriminant between signal and background. An
additional enhancement of the signal purity comes from
the application of a b-tagging algorithm. This analysis uses
the SECVTX algorithm [15] to identify (“tag”) jets that
most likely originate from the fragmentation of a b quark,
requiring the presence of particle trajectories (tracks) that
form reconstructable vertices significantly displaced from
the vertex of the pp̄ collision. These vertices need to be
found inside the jet cone, and jet energy corrections specific
to b-jets are applied to tagged jets. Only events with one,
two, or three tagged jets are kept, excluding larger
multiplicities to reduce the possible assignments of jets
to partons in the event reconstruction. When three b-tagged
jets are present, the three possible assignments with two
b-tagged jets and one light-flavor jet are considered.
The dominant backgrounds to the all-hadronic final state
come from the QCD production of heavy-quark pairs (bb̄
and cc̄) and from events with incorrectly tagged jets
associated with light quarks or gluons. Given the large
theoretical uncertainties on the QCD multijet production
cross section, it is preferable to infer the background from
the data directly. The “tag rate” is defined as the probability
of tagging a jet, parametrized in terms of jet ET , number of
tracks contained in the jet cone, and the number of
reconstructed primary vertices in the event. This tag rate
is obtained in a background-rich control sample with five jets
and is used to estimate the probability that a candidate event
from background contains a given number of tagged jets.
Before the b-tagging requirement is imposed, a probability is
calculated for each data event that one, two, or three jets
could be tagged as b-jets. The sum of these probabilities over
all pretagged data events represents the background prediction for the given tag category. Correction factors are
introduced to take into account correlations among jets
due to the presence of multiple b quarks in the same event.
The procedure, described in detail in Ref. [12], allows the
prediction of the expected amount of background in the
selected samples as well as the distributions of specific
measured variables, as discussed later.
The top-quark mass is measured using a “template
method” [16], while simultaneously (in situ) calibrating
the jet energy scale (JES) to reduce the associated systematic uncertainty. Reference distributions (“templates”) are
091101-4
RAPID COMMUNICATIONS
MEASUREMENT OF THE TOP-QUARK MASS IN THE ALL- …
derived for the signal from variables sensitive to the true
values of Mtop and JES. The chosen templates correspond
to the top-quark mass mrec
and the W-boson mass mrec
t
W ,
obtained from a kinematical reconstruction of the final
state. The JES is a multiplicative factor that, applied to the
raw energy of a reconstructed jet, returns a corrected energy
that is designed to give the best estimate of the energy of the
associated parton. The uncertainty on the JES value to be
applied in simulated events results in a large uncertainty on
the measurements of M top . A maximum likelihood fit is
then performed to find the M top and JES values that best
match the distributions observed in the data.
In this analysis the applied JES is expressed as a function
of the dimensionless parameter ΔJES, which measures the
shift ΔJES · σ c with respect the CDF default value. The latter
is based on a combination of instrumental calibration and
analysis of data control samples [14], and σ c represents
here its uncertainty.
For each selected event, mass combinations are generated [12] assigning in turn each one of the six highest-ET
jets to one of the final-state six quarks. Then, for each
combination, two triplets of jets are associated with the two
top quarks, each triplet including a pair of jets (corresponding to the W boson) and a b-tagged jet. The number of
possible combinations is reduced by assigning b-tagged
jets to b quarks only, resulting in 30, 6, or 18 permutations
for events with one, two, or three tagged jets, respectively.
For each combination, a value of mrec
t is obtained through
a constrained fit based on the minimization of a χ 2 -like
function defined as
ð1Þ
χ 2t ¼
ðmjj − MW Þ2 c4
Γ2W
ð2Þ
þ
ðmjj − MW Þ2 c4
Γ2W
ð1Þ
þ
þ
2 4
ðmjjb − mrec
t Þ c
Γ2t
6
meas 2
X
ðpfit
T;i − pT;i Þ
i¼1
ð1;2Þ
where mjj
σ 2i
left free to vary. Independent distributions for events with
exactly one or with two or three tags are built from the mrec
t
and mrec
W values.
Signal templates are formed using simulated events with
top-quark masses ranging from 167.5 to 177.5 GeV=c2 , in
steps of 1.0 GeV=c2 , and with ΔJES between −2 and þ2, in
steps of 0.5. Background templates are obtained applying the
fitting technique to the events passing the neural-network
selection, but before the b-tagging requirement (“pretag”
sample) [12]. The distributions are formed assigning to
rec
each value of mrec
t and mW a weight that is given by the
probability of the event to be from background and to
contain tagged jets, as evaluated from the jet tag rates. The
signal presence in the pretag sample is accounted for.
At this stage, two requirements are imposed on the events:
N out ≥ 0.97 (0.94) and χ 2W ≤ 2 (3) for 1 (≥ 2) tag events.
The events that survive these selection criteria comprise the
SJES sample, which is used primarily to constrain the
statistical uncertainty on the ΔJES measurement. A subset
of the SJES sample (SMtop ) is obtained by additionally
requiring χ 2t ≤ 3 (4) for 1 (≥ 2) tag events; the SMtop sample
is the primary set of events used to extract the top-quark
mass. The N out , χ 2W , χ 2t thresholds have been optimized to
minimize the statistical uncertainty on the Mtop measurement
based on simulations. The corresponding signal and backrec
ground events are then used to populate the mrec
W and mt
templates for the SJES and SMtop subsets, respectively.
Table I summarizes the event selection for events with
one tag and with two or three tags, separately.
The measurement of Mtop and the simultaneous calibration of JES are performed by maximizing an unbinned
extended-likelihood function. The function, defined in
detail in Ref. [8], is divided into three parts,
ð2Þ
þ
PHYSICAL REVIEW D 90, 091101(R) (2014)
L ¼ L1 tag × L≥2 tags × LΔJES;constr ;
2 4
ðmjjb − mrec
t Þ c
Γ2t
where LΔJES;constr is a Gaussian term constraining the JES to
the nominal value (i.e., ΔJES to 0) within its uncertainty.
The two terms L1 tag and L≥2 tags are in turn defined as
;
L1;≥2 tags ¼ LΔJES × LMtop × Levts ;
represent the invariant masses of the two pairs
ð1;2Þ
of jets assigned to light-flavor quarks, while mjjb represent
the invariant masses of the triplets including one light-flavor
pair and one jet assigned to a b quark. The quantities MW ¼
80.4 GeV=c2 and ΓW ¼ 2.1 GeV are the known measured
mass and width of the W boson [7], while Γt ¼ 1.5 GeV is
the estimated natural width of the top quark [17]. In the fit,
the transverse momenta of the jets pfit
T;i are constrained to
meas
their measured values pT;i within their known resolutions
σ i . Among all combinations, the one that gives the lowest
value for the minimized χ 2t is selected along with the value of
mrec
t determined by the fit. An additional fit is introduced for
2
the reconstruction of mrec
W , by defining a specific χ function,
χ 2W , where the known W-boson mass is replaced by mrec
W and
TABLE I. Numbers of candidate events (N obs ) and expected
signal yield in the two selected samples. For the signal, Mtop ¼
172.5 GeV=c2 and ΔJES ¼ 0 are used, and expectations are
normalized to the integrated luminosity of the data sample
(9.3 fb−1 ) using the theoretical cross section (7.46 pb [18]).
The uncertainty on the signal comes from the uncertainty on the
cross section and on the integrated luminosity.
Sample
1 tag
≥ 2 tags
091101-5
SJES
SMtop
SJES
SMtop
N obs
Expected tt̄
7890
4130
1758
901
1886 150
1270 101
782 64
514 42
RAPID COMMUNICATIONS
T. AALTONEN et al.
PHYSICAL REVIEW D 90, 091101(R) (2014)
where Levts gives the probability to observe simultaneously
the number of events selected in the SJES and the SMtop data
samples, given the expected signal and background yields.
Unlike the analysis in Ref. [8], the background yields are
allowed to vary unconstrained in the fit. The two terms
LΔJES and LMtop represent the likelihoods, based on the
signal and background templates, to observe the sets of mrec
W
and mrec
t values in the two data sets SJES and SMtop . For each
signal template, the probability density function (PDF) is
represented as a sum of gamma and Gaussian functions,
whose parameters are in turn linear functions of the fit
parameters M top and ΔJES . In Fig. 1, examples of signal
and background mrec
t templates for the sample with two or
three tags are shown, with the corresponding PDFs
superimposed.
The possible presence of biases in the values returned by
the likelihood fit is investigated and taken into account.
Fraction of events/2.5 GeV/c2
0.1
(a)
tt mrec
templates
t
≥ 2 tags events (Δ
JES
167.5
172.5
0.06
177.5
Ps(mrec)
t
0.04
0.02
0
120
140
160
180
200
220
Mtop ¼ 175.071.19ðstatÞ0.97ðJESÞ0.41ðfitÞ GeV=c2 ;
and
ΔJES ¼ −0.282 0.255ðstatÞ 0.207ðM top Þ 0.040ðfitÞ;
where the fit uncertainties are those arising from the variation
in the fitted signal and background yields, to which the
additional systematic uncertainties described below will be
added in quadrature. The correlation between M top and ΔJES
amounts to −0.63. The best-fit values of M top and ΔJES are
shown in Fig. 2, along with the negative log-likelihood
contours whose projections correspond to one, two, and
three σ uncertainties on the values of M top and ΔJES . The fit
returns, for the SMtop sample, a signal yield of 1244 114
(420 38) events with one (two or three) tag(s).
rec
The distributions of mrec
t and mW for the data and the
comparison with the expectation from the sum of background and signal for M top and ΔJES corresponding to the
= 0.0)
M top [GeV/c2]
0.08
Pseudoexperiments (PEs) are performed assuming specific
values for Mtop and ΔJES and “pseudodata” are extracted
from the corresponding signal and background templates
and subjected to the likelihood maximization procedure.
The results of these PEs are compared to the input values,
and linear calibration functions are defined to obtain, on
average, a more accurate estimate of the true values and
uncertainties. The average shift in top-quark mass due to
the calibration is about 200 MeV=c2 .
The likelihood fit is applied to the data, and after
applying the calibration corrections, the values returned
by the fit are
240
m rec
[GeV/c2]
t
≥ 1-tag events (9.3 fb-1)
rec
t
(b)
Background m
templates
1
≥ 2 tags events
0.05
0.5
0.04
Background
0.03
Pb(mrec)
t
ΔJES
Fraction of events/2.5 GeV/c2
1.5
0
-0.5
Fitted values
-Ln(L/Lmax) = 4.5
0.02
-Ln(L/Lmax) = 2.0
-1
-Ln(L/Lmax) = 0.5
0.01
-1.5
0
168
170
172
174
176
178
Mtop [GeV/c2]
120
140
160
180
200
220
240
m rec
[GeV/c2]
t
FIG. 1 (color online). Templates of mrec
t for events with two or
three tags and corresponding probability density functions superimposed. (a) The signal PDF Ps, for various values of Mtop and
ΔJES ¼ 0. (b) The background PDF Pb.
FIG. 2 (color online). Negative log-likelihood contours for the
likelihood fit performed for the M top and ΔJES measurement,
before calibration, for events with one, two, or three tags. The
minimum is shown along with the contours whose projections
correspond to one, two, and three σ uncertainties on the M top and
ΔJES measurements.
091101-6
RAPID COMMUNICATIONS
MEASUREMENT OF THE TOP-QUARK MASS IN THE ALL- …
500
TABLE II. Sources of systematic uncertainties on the Mtop and
ΔJES measurements. The total uncertainty is evaluated as the
quadrature sum of all contributions.
≥ 1-tag events
(a)
Data (9.3 fb-1)
Fitted bkg + tt
Events/5.0 GeV/c2
400
Source
Fitted bkg
Generator (hadronization)
Parton distribution functions
Initial/Final state radiation
Color reconnection
ΔJES fit
M top fit
Other free parameters of the fit
Templates sample size
tt̄ cross section
Integrated luminosity
Trigger
Background shape
b tagging
b-jets energy scale
Pileup
Residual JES
Residual bias/Calibration
Total
300
200
100
0
100 120 140 160 180 200 220 240 260 280
m rec
[GeV/c2]
t
Events/5.0 GeV/c2
900
≥ 1-tag events
(b)
800
Data (9.3 fb-1)
700
Fitted bkg + tt
Fitted bkg
600
PHYSICAL REVIEW D 90, 091101(R) (2014)
σ Mtop (GeV=c2 )
σ ΔJES
0.29
0.273
þ0.18
−0.36
þ0.096
−0.052
0.13
0.32
0.97
0.41
0.34
0.15
0.15
0.61
0.15
0.04
0.20
0.22
0.57
0.232
0.101
0.207
0.040
0.071
0.034
0.032
0.188
0.014
0.018
0.035
0
þ0.27
−0.24
þ1.55
−1.58
þ0.077
−0.096
þ0.492
−0.488
500
400
300
200
100
0
20
40
60
80 100 120 140 160 180 200 220
2
m rec
W [GeV/c ]
rec
FIG. 3 (color online). Distributions of (a) mrec
t and (b) mW for
events with one, two, or three tags (black dots), compared to the
distributions from background and signal corresponding to the
measured values of M top and ΔJES . The expected distributions are
normalized to the yields returned by the best fit.
measured values are shown in Fig. 3. The contributions
from events with one, two, or three tags are summed
together and the signal and background yields are normalized to the yields returned by the best fit.
The measurements of Mtop and ΔJES are affected by
various sources of systematic uncertainties, summarized in
Table II. These uncertainties can be divided into four
categories: (1) the modeling of signal events, including
the choice of Monte Carlo generator and parton distribution
function, the amount of initial and final state radiation, and
the effects of color reconnections; (2) the measurement
method, including the dependence on the other free
parameters of the fit, the size of the samples used to build
the reference templates, the variables used to perform
calibration PEs like the tt̄ production cross section and
the integrated luminosity of the data, and the trigger
simulation; (3) the background modeling, the b-tagging
efficiency, the effects of multiple hadron interactions
(pileup) related to the instantaneous luminosity; and
(4) the jet energy scale calibration. The largest contribution
comes from the jet energy scale calibration, given the
large number of jets representing a typical feature of the allhadronic channel. With respect to Ref. [12] we add in this
analysis the uncertainties related to the background shape
(and not to its normalization) to the tt̄ cross section and to
the integrated luminosity. In general, the uncertainties are
evaluated by performing PEs based on templates made with
specific variations of the original signal samples, taking the
differences in the average values of M top and ΔJES with
respect to the pseudoexperiments performed with default
templates. Finally, possible residual biases remaining after
the calibration and uncertainties on the parameters of the
calibration functions are taken into account.
In summary, a measurement of the top-quark mass using
top-quark pairs decaying into a fully hadronic final state is
presented, using pp̄ collision data corresponding to the full
integrated luminosity of 9.3 fb−1 collected by the CDF
experiment in Run II. The large background affecting this
channel is strongly suppressed through an optimized event
selection, based on a neural network and the requirement
of one, two, or three jets originating from b quarks. The
simultaneous calibration of the jet energy scale allows
us to reduce the systematic uncertainty due to this source
to 0.97 GeV=c2 . The measured value of the top-quark
2
mass is M top ¼ 175.07 1.19ðstatÞ þ1.55
−1.58 ðsystÞ GeV=c ,
with a total uncertainty of approximately 2.0 GeV=c2,
091101-7
RAPID COMMUNICATIONS
T. AALTONEN et al.
PHYSICAL REVIEW D 90, 091101(R) (2014)
corresponding to a 1.1% relative uncertainty. This final
result in the all-hadronic channel is complementary to the
most recent measurements obtained in other channels by
the CDF Collaboration [19,20], and consistent with the
CMS measurement in the same channel [21].
We thank the Fermilab staff and the technical staffs of the
participating institutions for their vital contributions. This
work was supported by the U.S. Department of Energy and
National Science Foundation; the Italian Istituto Nazionale
di Fisica Nucleare; the Ministry of Education, Culture,
Sports, Science and Technology of Japan; the Natural
Sciences and Engineering Research Council of Canada;
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